39
7/29/2019 The First 498 Bernoulli Numbers (Plouffe) http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 1/39 *The Project GutenbergEtext of Thefirst 498Bernoulli Numbers* #22 in our seriesof math constants Copyright laws are changing all over the world, be sure to check the copyright laws for your country before posting these files!! Please take a look at the important information in this header. We encourage you to keep this file on your own disk, keeping an electronic path open for the next readers. Do not remove this. **Welcome To The World of Free Plain Vanilla Electronic Texts** **Etexts Readable By Both Humans and By Computers, Since 1971** *These Etexts Prepared By Hundreds of Volunteers and Donations* Information on contactingProject Gutenberg to get Etexts, and further information is included below. We need your donations.  Title: The first 498 Bernoulli Numbers Editor: Simon Plouffe April, 2001[Etext #2586] *The Project Gutenberg Etext of The first 498 Bernoulli Numbers* ******This file should be named brnll10.txt or brnll10.zip****** Corrected EDI TI ONS of our etexts get a new NUMBER, brnll11.txt VE RSIONS based on separate sources get new LETTER, brnll10a.txt Mathematical constants and numbers edited by Simon Plouffe Associate Professor LaCIM, University of Quebec at Montreal http://www.lacim.uqam.ca/pi : Plouffe's Inverter [email protected] Project Gutenberg Etexts are usually created from multiple editions, all of which are in the Public Domain in the United States, unless a copyright notice is included. Therefore, we usually do NOT keep any of these books in compliance with any particular paper edition. We are now tryingto release all our books one month in advance of the official release dates, leavingtime for better editing. file:///C:/Users/Feli peCruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number... 1 de39 10/03/2013 07:36 a.m.

The First 498 Bernoulli Numbers (Plouffe)

Embed Size (px)

Citation preview

Page 1: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 1/39

*The Project Gutenberg Etext of The first 498 Bernoulli Numbers* #22 in our series of math constants

Copyright laws are changing all over the world, be sure to check the copyright laws for your country before posting these files!!

Please take a look at the important information in this header. We encourage you to keep this file on your own disk, keeping an electronic path

open for the next readers. Do not remove this.

**Welcome To The World of Free Plain Vanilla Electronic Texts**

**Etexts Readable By Both Humans and By Computers, Since 1971**

*These Etexts Prepared By Hundreds of Volunteers and Donations*

Information on contacting Project Gutenberg to get Etexts, and further information is included below. We need your donations.

 Title: The first 498 Bernoulli Numbers

Editor: Simon Plouffe

April, 2001 [Etext #2586]

*The Project Gutenberg Etext of The first 498 Bernoulli Numbers*******This file should be named brnll10.txt or brnll10.zip******

Corrected EDITIONS of our etexts get a new NUMBER, brnll11.txtVERSIONS based on separate sources get new LETTER, brnll10a.txt

Mathematical constants and numbers edited by Simon Plouffe Associate Professor LaCIM, University of Quebec at Montrealhttp://www.lacim.uqam.ca/pi : Plouffe's Inverter [email protected]

Project Gutenberg Etexts are usually created from multiple editions, all of which are in the Public Domain in the United States, unless a copyrightnotice is included. Therefore, we usually do NOT keep any of these books in compliance with any particular paper edition.

We are now trying to release all our books one month in advance of the official release dates, leaving time for better editing.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

1 de 39 10/03/2013 07:36 a.m.

Page 2: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 2/39

Please note: neither this list nor its contents are final till midnight of the last day of the month of any such announcement. The official release dateof all Project Gutenberg Etexts is at Midnight, Central Time, of the last day of the stated month. A preliminary version may often be posted forsuggestion, comment and editing by those who wish to do so. To be sure you have an up to date first edition [xxxxx10x.xxx] please check file sizesin the first week of the next month. Since our ftp program has a bug in it that scrambles the date [tried to fix and failed] a look at the file size willhave to do, but we will try to see a new copy has at least one byte more or less.

Information about Project Gutenberg (one page)

We produce about two million dollars for each hour we work. The time it takes us, a rather conservative estimate, is fifty hours to get any etextselected, entered, proofread, edited, copyright searched and analyzed, the copyright letters written, etc. This projected audience is one hundredmillion readers. If our value per text is nominally estimated at one dollar then we produce $2 million dollars per hour this year as we releasethirty-six text files per month, or 432 more Etexts in 1999 for a total of 2000+If these reach just 10% of the computerized population, then thetotal should reach over 200 billion Etexts given away this year.

 The Goal of Project Gutenberg is to Give Away One Trillion Etext Files by December 31, 2001. [10,000 x 100,000,000 =1 Trillion] This is tenthousand titles each to one hundred million readers, which is only ~5% of the present number of computer users.

At our revised rates of production, we will reach only one-third of that goal by the end of 2001, or about 3,333 Etexts unless we manage to getsome real funding; currently our funding is mostly from Michael Hart's salary at Carnegie-Mellon University, and an assortment of sporadic gifts;this salary is only good for a few more years, so we are looking for something to replace it, as we don't want Project Gutenberg to be so dependenton one person.

We need your donations more than ever!

All donations should be made to "Project Gutenberg/CMU": and are tax deductible to the extent allowable by law. (CMU = Carnegie- MellonUniversity).

For these and other matters, please mail to:

Project GutenbergP. O. Box 2782Champaign, IL 61825

When all other email fails. . .try our Executive Director: Michael S. Hart <[email protected]> [email protected] forwards to [email protected] archive.org if your mail bounces from archive.org, I will still see it, if it bounces from prairienet.org, better resend later on. . . .

We would prefer to send you this information by email.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

2 de 39 10/03/2013 07:36 a.m.

Page 3: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 3/39

******

 To access Project Gutenberg etexts, use any Web browser to view http://promo.net/pg. This site lists Etexts by author and by title, and includesinformation about how to get involved with Project Gutenberg. You could also download our past Newsletters, or subscribe here. This is one of ourmajor sites, please email [email protected], for a more complete list of our various sites.

 To go directly to the etext collections, use FTP or any Web browser to visit a Project Gutenberg mirror (mirror sites are available on 7 continents;

mirrors are listed at http://promo.net/pg).

Mac users, do NOT point and click, typing works better.

Example FTP session:

ftp metalab.unc.edu login: anonymous password: your@login cd pub/docs/books/gutenberg cd etext90 through etext99 dir [to see files] get or mget[to get files. . .set bin for zip files] GET GUTINDEX.?? [to get a year's listing of books, e.g., GUTINDEX.99] GET GUTINDEX.ALL [to get alisting of ALL books]

***

**Information prepared by the Project Gutenberg legal advisor**

(Three Pages)

***START**THE SMALL PRINT!**FOR PUBLIC DOMAIN ETEXTS**START*** Why is this "Small Print!" statement here? You know:lawyers. They tell us you might sue us if there is something wrong with your copy of this etext, even if you got it for free from someone other thanus, and even if what's wrong is not our fault. So, among other things, this "Small Print!" statement disclaims most of our liability to you. It also tellsyou how you can distribute copies of this etext if you want to.

*BEFORE!* YOU USE OR READ THIS ETEXT By using or reading any part of this PROJECT GUTENBERG-tm etext, you indicate that youunderstand, agree to and accept this "Small Print!" statement. If you do not, you can receive a refund of the money (if any) you paid for this etextby sending a request within 30 days of receiving it to the person you got it from. If you received this etext on a physical medium (such as a disk),you must return it with your request.

ABOUT PROJECT GUTENBERG-TM ETEXTS This PROJECT GUTENBERG-tm etext, like most PROJECT GUTENBERG- tm etexts, is a"public domain" work distributed by Professor Michael S. Hart through the Project Gutenberg Association at Carnegie-Mellon University (the"Project"). Among other things, this means that no one owns a United States copyright on or for this work, so the Project (and you!) can copy anddistribute it in the United States without permission and without paying copyright royalties. Special rules, set forth below, apply if you wish to copy

and distribute this etext under the Project's "PROJECT GUTENBERG" trademark.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

3 de 39 10/03/2013 07:36 a.m.fil li k i i h i ll i b

Page 4: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 4/39

 To create these etexts, the Project expends considerable efforts to identify, transcribe and proofread public domain works. Despite these efforts,the Project's etexts and any medium they may be on may contain "Defects". Among other things, Defects may take the form of incomplete,inaccurate or corrupt data, transcription errors, a copyright or other intellectual property infringement, a defective or damaged disk or other etextmedium, a computer virus, or computer codes that damage or cannot be read by your equipment.

LIMITED WARRANTY ; DISCLAIMER OF DAMAGES But for the "Right of Replacement or Refund" described below, [1] the Project (and anyother party you may receive this etext from as a PROJECT GUTENBERG-tm etext) disclaims all liability to you for damages, costs and expenses,

including legal fees, and [2] YOU HAVE NO REMEDIES FOR NEGLIGENCE OR UNDER STRICT LIABILITY, OR FOR BREACH OFWARRANTY OR CONTRACT, INCLUDING BUT NOT LIMITED TO INDIRECT, CONSEQUENTIAL, PUNITIVE OR INCIDENTALDAMAGES, EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH DAMAGES.

If you discover a Defect in this etext within 90 days of receiving it, you can receive a refund of the money (if any) you paid for it by sending anexplanatory note within that time to the person you received it from. If you received it on a physical medium, you must return it with your note,and such person may choose to alternatively give you a replacement copy. If you received it electronically, such person may choose toalternatively give you a second opportunity to receive it electronically.

 THIS ETEXT IS OTHERWISE PROVIDED TO YOU "AS-IS". NO OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, ARE MADE TO YOU AS TO

 THE ETEXT OR ANY MEDIUM IT MAY BE ON, INCLUDING BUT NOT LIMITED TO WARRANTIES OF MERCHANTABIL ITY OR FITNESS FOR APARTICULAR PURPOSE.

Some states do not allow disclaimers of implied warranties or the exclusion or limitation of consequential damages, so the above disclaimers andexclusions may not apply to you, and you may have other legal rights.

INDEMNITY You will indemnify and hold the Project, its directors, officers, members and agents harmless from all liability, cost and expense,including legal fees, that arise directly or indirectly from any of the following that you do or cause: [1] distribution of this etext, [2] alteration,modification, or addition to the etext, or [3] any Defect.

DISTRIBUTION UNDER "PROJECT GUTENBERG-tm" You may distribute copies of this etext electronically, or by disk, book or any othermedium if you either delete this "Small Print!" and all other references to Project Gutenberg, or:

[1] Only give exact copies of it. Among other things, this requires that you do not remove, alter or modify the etext or this "small print!" statement. You may however, if you wish, distribute this etext in machine readable binary, compressed, mark-up, or proprietary form, including any formresulting from conversion by word pro- cessing or hypertext software, but only so long as *EITHER*:

[*] The etext, when displayed, is clearly readable, and does *not* contain characters other than those intended by the author of the work, although tilde (~), asterisk (*) and underline (_) characters may be used to convey punctuation intended by the author,and additional characters may be used to indicate hypertext links; OR

[*] The etext may be readily converted by the reader at no expense into plain ASCII, EBCDIC or equivalent form by the program

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

4 de 39 10/03/2013 07:36 a.m.fil ///C /U /F li C /D kt /VARIOS it i / MB/Th Fi t498B ll i N b

Page 5: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 5/39

that displays the etext (as is the case, for instance, with most word processors); OR

[*] You provide, or agree to also provide on request at no additional cost, fee or expense, a copy of the etext in its original plainASCII form (or in EBCDIC or other equivalent proprietary form).

[2] Honor the etext refund and replacement provisions of this "Small Print!" statement.

[3] Pay a trademark license fee to the Project of 20% of the net profits you derive calculated using the method you already use to calculate yourapplicable taxes. If you don't derive profits, no royalty is due. Royalties are payable to "Project Gutenberg Association/Carnegie-MellonUniversity" within the 60 days following each date you prepare (or were legally required to prepare) your annual (or equivalent periodic) taxreturn.

WHAT IF YOU *WANT* TO SEND MONEY EVEN IF YOU DON'T HAVE TO? The Project gratefully accepts contributions in money, time,scanning machines, OCR software, public domain etexts, royalty free copyright licenses, and every other sort of contribution you can think of.Money should be paid to "Project Gutenberg Association / Carnegie-Mellon University".

We are planning on making some changes in our donation structure in 2000, so you might want to email me, [email protected] beforehand.

*END THE SMALL PRINT! FOR PUBLIC DOMAIN ETEXTS*Ver.04.29.93*END*

Mathematical constants and numbers edited by Simon Plouffe Associate Professor LaCIM, University of Quebec at Montrealhttp://www.lacim.uqam.ca/pi : Plouffe's Inverter [email protected]

 The first 498 Bernoulli numbers are the coefficients of the series expansion of 

t*exp(x*t)/(exp(t)-1) =sum( B(n,x)/n!*t̂ n, n=0..infinity ).

Bernoulli(2) 1/6

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

5 de 39 10/03/2013 07:36 a.m.fil ///C /U /F li C /D kt /VARIOS it i / MB/Th Fi t498B ll i N b

Page 6: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 6/39

Bernoulli(4) -1/30

Bernoulli(6) 1/42

Bernoulli(8) -1/30

Bernoulli(10) 5/66

Bernoulli(12) -691/2730

Bernoulli(14) 7/6

Bernoulli(16) -3617/510

Bernoulli(18) 43867/798

Bernoulli(20) -174611/330

Bernoulli(22) 854513/138

Bernoulli(24) -236364091/2730

Bernoulli(26) 8553103/6

Bernoulli(28) -23749461029/870

Bernoulli(30) 8615841276005/14322

Bernoulli(32) -7709321041217/510

Bernoulli(34) 2577687858367/6

Bernoulli(36) -26315271553053477373/1919190

Bernoulli(38) 2929993913841559/6

Bernoulli(40) -261082718496449122051/13530

Bernoulli(42) 1520097643918070802691/1806

Bernoulli(44) -27833269579301024235023/690

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

6 de 39 10/03/2013 07:36 a.m.

file ///C /Users/FelipeCruz/Desktop/VARIOS escritorio/ MB/TheFirst498Bernoull i Number

Page 7: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 7/39

Bernoulli(46) 596451111593912163277961/282

Bernoulli(48) -5609403368997817686249127547/46410

Bernoulli(50) 495057205241079648212477525/66

Bernoulli(52) -801165718135489957347924991853/1590

Bernoulli(54) 29149963634884862421418123812691/798

Bernoulli(56) -2479392929313226753685415739663229/870

Bernoulli(58) 84483613348880041862046775994036021/354

Bernoulli(60) -1215233140483755572040304994079820246041491/56786730

Bernoulli(62) 12300585434086858541953039857403386151/6

Bernoulli(64) -106783830147866529886385444979142647942017/510

Bernoulli(66) 1472600022126335654051619428551932342241899101/64722

Bernoulli(68) -78773130858718728141909149208474606244347001/30

Bernoulli(70) 1505381347333367003803076567377857208511438160235/4686

Bernoulli(72) -5827954961669944110438277244641067365282488301844260429/140100870

Bernoulli(74) 34152417289221168014330073731472635186688307783087/6

Bernoulli(76) -24655088825935372707687196040585199904365267828865801/30

Bernoulli(78) 414846365575400828295179035549542073492199375372400483487/3318

Bernoulli(80) -4603784299479457646935574969019046849794257872751288919656867/230010

Bernoulli(82) 1677014149185145836823154509786269900207736027570253414881613/498

Bernoulli(84) -2024576195935290360231131160111731009989917391198090877281083932477/3404310

Bernoulli(86) 660714619417678653573847847426261496277830686653388931761996983/6

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

7 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/FelipeCruz/Desktop/VARIOS escritorio/ MB/TheFirst498Bernoull i Number

Page 8: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 8/39

Bernoulli(88) -1311426488674017507995511424019311843345750275572028644296919890574047/61410

Bernoulli(90) 1179057279021082799884123351249215083775254949669647116231545215727922535/ 272118

Bernoulli(92) -1295585948207537527989427828538576749659341483719435143023316326829946247/1410

Bernoulli(94) 1220813806579744469607301679413201203958508415202696621436215105284649447/6

Bernoulli(96) -211600449597266513097597728109824233673043954389060234150638733420050668349987 259/4501770

Bernoulli(98) 67908260672905495624051117546403605607342195728504487509073961249992947058239/6

Bernoulli(100) -945980378191221252952274330694937218727028415330669361333856962043113954151972 47711/33330

Bernoulli(102) 3204019410860907078243020782116241775491817197152717450679002501086861530836678 158791/4326

Bernoulli(104) -319533631363830011287103352796174274671189606078272738327103470162849568365549 721224053/1590

Bernoulli(106) 3637390317261741440815182015159342716923129864058169003893081637828187987338620 2346572901/642

Bernoulli(108) -3469342247847828789552088659323852541399766785760491146870005891371501266319724897592306597338057/209191710

Bernoulli(110) 7645992940484742892248134246724347500528752413412307906683593870759797606269585 779977930217515/1518

Bernoulli(112) -2650879602155099713352597214685162014443151499192509896451788427680966756514875515366781203552600109/1671270

Bernoulli(114) 2173783231936916333331076108665299147572115667909083136080611011493360548423459 3650904188618562649/42

Bernoulli(116) -309553916571842976912513458033841416869004128064329844245504045721008957524571968271388199595754752259/1770

Bernoulli(118) 3669631199697131115349471515855850066846063610806992043010594406764144850458064 61889371776354517095799/6

Bernoulli(120) -51507486535079109061843996857849983274095170353262675213092869167199297474922985358811329367077682677803282070131/2328255930

Bernoulli(122) 4963366607926258191253263747599075743872279031106013977030931179315068321410043

1329033113678098037968564431/6

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

8 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/FelipeCruz/Desktop/VARIOS escritorio/ MB/TheFirst498Bernoull i Number

Page 9: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 9/39

Bernoulli(124) -95876775334247128750774903107542444620578830013297336819553512729358593354435944413631943610268472689094609001/30

Bernoulli(126) 5556330281949274850616324408918951380525567307126747246796782304333594286400508981287241419934529638692081513802696639/4357878

Bernoulli(128) -267754707742548082886954405585282394779291459592551740629978686063357792734863

530145362663093519862048495908453718017/510

Bernoulli(130) 1928215175136130915645299522271596435307611010164728458783733020528548622403504078595174411693893882739334735142562418015/8646

Bernoulli(132) -410951945846993378209020486523571938123258077870477502433469747962650070754704863812646392801863686694106805747335370312946831/4206930

Bernoulli(134) 264590171870717725633635737248879015151254525593168688411918554840667765591690540727987316391252434348664694639349484190167/6

Bernoulli(136) -84290226343367405131287578060366193649336612397547435767189206912230442242628212786558235455817749737691517685781164837036649737/4110

Bernoulli(138) 2694866548990880936043851683724113040849078494664282483862150893060478501559546243423633375693325757795709438325907154973590288136429/274386

Bernoulli(140) -3289490986435898803930699548851884006880537476931130981307467085162504802973618096693859598125274741604181467826651144393874696601946049/679470

Bernoulli(142) 1473185328088858956587008044245321423980421702399064267619487899740754606158164

3106569966189211748270209483494554402556608073385149191/6

Bernoulli(144) -3050244698373607565035155836901726357405007104256566761884191852434851033744761276392695669329626855965183503295793517411526056244431024612640493/2381714790

Bernoulli(146) 4120570026280114871526113315907864026165545608808541153973817680034790262683524284855810008621905238290240143481403022987037271683989824863/6

Bernoulli(148) -1691737145614018979865561095112166189607682852147301400816480675916957871178648433284821493606361235973346584667336181793937950344828557898347149/4470

Bernoulli(150) 4633655793891627414432844258118062649822337254252957998522998073253793155015723

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

9 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/FelipeCruz/Desktop/VARIOS escritorio/ MB/TheFirst498Bernoull i Number

Page 10: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 10/39

05760030594769688296308375193913787703707693010224101613904227979066275/2162622

Bernoulli(152) -3737018141155108502105892888491282165837489531488932951768507127182409731328472084456653639812530140212355374618917309552824925858430886313795805601/30

Bernoulli(154) 10259718682038021051027794238379184461025738652460569233992776489750881337506863808448685054322627708245455888249006715516690124228801409697850408284121/138

Bernoulli(156) -8171808608326262851075645975367345231359571039611646758215209059609254869913834694299550948828465080397683633716467049473386655982976884836350662433481896141 9869/1794590070

Bernoulli(158) 171672676901153210072183083506103395137513922274029564150500135265308148197358551999205867870374013289728260984269623579880772408522396975250682773558018919/6

Bernoulli(160) -4240860794203310376065563492361156949989398087086373214710625778458441940477839981850928830420029285687066701804645453159767402961229305942765784122421197736 180867/230010

Bernoulli(162) 1584451495144416428390934243279426140836596476080786316960222380784239380974799

8803643636479781686345904182158544197937165493888659053485343756299287320087862 33507729/130074

Bernoulli(164) -2053806460914321626557197958669264683780533102314864506813337238393034494831660059120392638854094081483317332279380432508494509482852486062609201354728133535 6200073083/2490

Bernoulli(166) 57340329693708609216310953113926457315052223585552084985730889113030017846521229647032057527091941930952463086112641216788342507044680826483137881247541686718 15815821441/1002

Bernoulli(168) -1384482851517639608123834658506351722853110915698434524926045393431777275483679125898751654032498361156975864952598334740858904573417658927014305850902639224 6407576578281097477/3404310

Bernoulli(170) 19533420762663753041497677923846223448141033735098842721513999570734697912468691826768817153635265057253533036981817697995193147742759487278301874989469915791 7782460035894085/66

Bernoulli(172) -1144370221133332844718717994299184661300804650603242173175525814866528783226493102478136596263330170177308847084162180432820100802012999695554946757321765958 7609679405537739509973/5190

Bernoulli(174) 41661615546620428318849595932507172973956143181825614120481806840774078033175912708311946192938321074824269456551433579098072518528592794831763734356976076398 83085093246499347128331/2478

Bernoulli(176) -1369347910486705707645621362512824332220360774476594348356938715366608044588614657557436131706543948464159947970464346070253278291989696390096800799614617317 655510118710460076077638883999/1043970

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

10 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/FelipeCruz/Desktop/VARIOS - escritorio/ MB/TheFirst498Bernoull i Number

Page 11: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 11/39

Bernoulli(178) 11242518166179412900264848512062999827747204677128672752920437016188298267083957454596541707183631821434183145140854266928570184286149354127360639468530330943 28968069656979232446257101741/1074

Bernoulli(180) -6173136454016248924640522272263470960199559328290655337530202055853397791747341312347030141906500993752700612233695954532816018207721731818225290076670213481102834647254685911917265818955932383093313/7225713885390

Bernoulli(182) 42772692793491925411373044006286293483274681358284022916616830186224516599895955107129158104362387211395469635586552603843289887732196880914435296265313356879 51612545946030357929306651006711/6

Bernoulli(184) -857321333523056180131194437347933216431403305730705359015465649285681432317514010686029079324479659634642384809061711319481020030715989009140595170556956196762318625529645723516532076273012244047/1410

Bernoulli(186) 22258646098436968050639602221816385181596567918515338169946670500599612225742487595012775838387331550474751212260636163500086787417640903770807353228157478339547041472679880890292167353534100797481/42

Bernoulli(188) -14158277750623758793309386870401397333112823632717478051426522029712001260747920789473711562165031101665618225654329210473605281619696918061316240634857984019071572591940586875558943580878119388321001/30

Bernoulli(190) 5411555842544259796131885546196787277987837486638756184149141588783989774511509608733429067517383750706299486822702171672522203106730993581242777825864203487238429479957280273093904025319950569633979493395/12606

Bernoulli(192) -3464657529975826996901914057509523668719231923409555934864857153703921548941020004069801625217284925019175980127114021635301665169911151221313985420290562869

59857727373568402417020319761912636411646719477318166587/868841610

Bernoulli(194) 2269186825161532962833665086968359967389321429297588337232986752409765414223476696863199759981611817660735753831323900456495253961837175924312108872915089534970310604331636484174526399721365966337809334021247/6

Bernoulli(196) -62753135110461193672553106699893713603153054153311895305590639107017824640241378480484625554578576142115835788960865534532214560982925549798683762705231316611716668749347221458005671217067357943416524984438771831113/171390

Bernoulli(198) 88527914861348004968400581010530565220544526400339548429439843908721196349579494069282285662653465989920237253162555666526385826449862863083834096823053048072

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

11 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/FelipeCruz/Desktop/VARIOS - escritorio/ MB/TheFirst498Bernoull i Number

Page 12: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 12/39

002986184254693991336699593468906111158296442729034119206322233/244713882

Bernoulli(200) -498384049428333414764928632140399662108495887457206674968055822617263669621523687568865802302210999132601412697613279391058654527145340515840099290478026350382802884371712359337984274122861159800280019110197888555893671151/1366530

Bernoulli(202) 2250525326187264545900714460628885135841050444551247116222631411681549780530233

516069957534394574922579290608180427520318235621123686109474343887857944611842438698399885295153935574958275021715116120056995036417537079471/6

Bernoulli(204) -110636644250856903590976481422794879200517231299540994715372334521128669716264196333811025709747746193210786820114369025849897345722531098042760530922656878891556664782168465095563132092311332073097630676251482491663634626858373/281190

Bernoulli(206) 2525292668891404920279427026668969389456388249389889339455604316691573384284678293620100066924361693666444722338743839198221347931651916807651198800935942493038194104759967208073711284671045255047521429204396148980705984836743/6

Bernoulli(208) -12407390668433023412711473483696990726334795896412761472587854072142800403373577087021298541061094633377354326966623278849423631924808044397822651135905640812063181221280972334965193338438214107578486417026806166184210160001817890901/ 27030

Bernoulli(210) 470818136852949261411064419795183731720261060834125720420669319524124520436082287591061301043357213322783174109726161883320653751919888581225434721915048200554342299722544020404147351818763644224133262180471896777520393840396571039563276 2155/9225988926

Bernoulli(212) -1856110669947388268389361040689764027464160460436671923253131176853224087741924378432403442710398247642246902212818749685974336641529240178398124235555437625

2514810445260249103561318190166700479496616365399646623703756226308633271686963 07/3210

Bernoulli(214) 400574893007015286193582676647685618070647722744862226804205274524579824253977054633978989954616034159006910946702351708557861898605596918720273187827168543246070884111850631094386559256879136029424445176574691180899448206378373069370360 7/6

Bernoulli(216) -11993122770108617858536443322964878003618156069559794803117809279608039120818829088000103355036592864877954563564831932363414886811786054601318517206937549605059298307895591515771731031691422489377098686236263367916404512751010916862894 129855138281961/15270994830

Bernoulli(218) 56464136440235235314726597295525749117636867808717003756274266633665078371223539970758917367068113376982486608387542434867781903315227859036615564586511750614

file:///C:/Users/Felipe Cruz/Desktop/VARIOS escritorio/_MB/The First 498 Bernoull i Number...

12 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/FelipeCruz/Desktop/VARIOS - escritorio/ MB/TheFirst498Bernoull i Number

Page 13: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 13/39

6982520482120661127399025066364738126136065995051973573092520211760615067217012 7523599/6

Bernoulli(220) -87170648099600746513320436797965444744200531896218032099411547648772425755796175401851663060948525022237381261119516125256279105175010815762022647701785466087109374740057429699502124049557324731984516230241089343734886411617511589017123 23446768306053/7590

Bernoulli(222) 1336805315855217266521085253935989334036987065195149797611188289129665000800395

51721607924572293763209936868177554094363992682910953502959686573810881682191334902779142690647238320626154317300612246499805666932586030993409969885423019145 19271322675688591/9366

Bernoulli(224) -30182400150813920876209786883119253803999832296331202688726959118075629821111540532358200501688299221894019647557759482607244015423197995662377459862455981022551919229357426105082809664626440225408396198610910490931293597990537815431954 92373882916779852781709/1671270

Bernoulli(226) 316822110890340167043687855821573489332284954078120873879667247398427248439631784959697863027203134202419468987146791618689819277126743898222871052507988695629510619743140121735789346089722138141066738563604926458338074963177669112159201 6493432807733153743581/1362

Bernoulli(228) -19065029099978881661232019231773858335677290391514131438762718705990577044459391560757189726242357646571020749026107377290275176746326095623878416587092660143290054075335219507444491098072158087702012477249322314952529816329080423713079 65561986133763291349835081839/625170

Bernoulli(230) 126207370449098185618328560903555556240168873196052617629976895710626466497451075324826322131529482994911229776907026423863777067999895653205384330726232521594641159180572947113966254365067360415424033700252584772051018080635940567599772 72469883621048184279331863155/3102

Bernoulli(232) -2277782962749544647786193093844710000584561145527861043594866852071596440076587235747852022645695523676561694856919437156369375152041285055935622032497285897

151359345040171955786899011718891877065760345722163063921177723102631428767500963315657655779698470644544064472947/412410

Bernoulli(234) 480867224771001697116513683699011649496855159878152931805742068517626950204279499281932407966997815888727039144001177194783700618900740782637516562256421883686495287564849123342843286211825800198337962453448529082007644439295666002669973893196613894216505936316966183107269/63042

Bernoulli(236) -3214671335909365893983805720031961907980006283474436636740192043610340393150143708698849729814044608882728557732330801864852303165442465411683644683436319692

2548032479902806701562176993971844341971211085796540917994745699497068700513404

file:///C:/Users/Felipe Cruz/Desktop/VARIOS escritorio/_MB/The First 498 Bernoull i Number...

13 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/FelipeCruz/Desktop/VARIOS - escritorio/ MB/TheFirst498Bernoull i Number...

Page 14: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 14/39

2835903494172569465751671057323145801/30

Bernoulli(238) 21954828084819816230623427376391154946628510524415478471365831649487269438565442138452375719697629394886161086199009071745032148355699097673730377547354631757000924688032674454208386076360699273002129330161098228962653466112032300056534380609136268347425707537340996253935261001/1434

Bernoulli(240) -212191008579182060478563837945461872287372869333130175188325135660897759482730035448146388858205966593247205572842356279587190846758925659038643395344396334821348861518596112373605365460921821915409949436456394757252173113308288776951844012432992719925522001911419529928297005743854184672707/9538864545210

Bernoulli(242) 4535049728315239205021018362829154800039522502549714840841943960634084990270225535043892135549408608572877513963384530325758104248133124392959997485849004663162061065909846598215984547677506961593292880902830325868627515047168286738527241360778218692535254144583771935549805772798793/138

Bernoulli(244) -1480677868678810347062135814574727890490996459903153909612611791768134015908900253197632543925157559965099005581639883558125985134242978146873558628010545299879178299856929100217178891524159543673803785481607540954533057560554704283718320006046424881681934129216249889269701182688055001/30

Bernoulli(246) 262668605206102118430195944953058387315319589613263079853189811674338644589939356676047394737425651989092115424635212785341601958591806782599345416064945113338168378810138043832891536358769753916174695061208903056552776976154338169779827414504134808495078925108569042616724875466536400029203/3486

Bernoulli(248) -350744554637525331834266774194965125351698611334967218009546875814550592113317

2244240023419466113277413785800736682458966212429373095894934752041434119711352215164597094886530278429206637066302031501412499166263642447542289785723225064437740655097573160922291075175522551466276032634749948001/30

Bernoulli(250) 3053985414762198703102020975667535181880294373982570358384262712216099013630127381226064671248970168701164841859177635139561220373102316273710980757409295039231697360536736113380473515993580188204966808323201772081668695321316425977503713933894934399351348240918411922863059423248058823372368106375/16566

Bernoulli(252) -897742888716303078436445205805986526326135594094133440338930199388988621138764

4018394330772429050916553981576435425458416217690946397167518935169971718945495

file:///C:/Users/Felipe Cruz/Desktop/VARIOS escritorio/_MB/The First 498 Bernoull i Number...

14 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/FelipeCruz/Desktop/VARIOS - escritorio/ MB/TheFirst498Bernoull i Number...

Page 15: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 15/39

9415964995262823025743004001915975128242680213612581748367743077774468104545056300803334120339537905702856877606246855867891786763741486735368783092237/ 303940201110

Bernoulli(254) 2884759276650094186013272224259584433367802183845217969121665253431996536437413850716488026971480747022580182931940812035472752343853999483816456012957551120812115224018480617695398681102870535795278832047330709610952952566962354787854087985127629191094880078635434933391568643930279007460403102076327/6

Bernoulli(256) -104203435297641800915507592803138769896333127491490532929531166632958450572751929026080533456531382568746630428805839898606131705503722712567379172835813497582706763790263297372586804372654090271412733654409742029405259156130663560412599913831518338400385290760913773448329773518728092595019422753511174189569/ 131070

Bernoulli(258) 56081693586889462275051589447484617682656486262465693822181172785524218338951641908717980184709547885060218908068568000776767834360070429300833879662707069272458173745883316346369196270761641325176838738153606175963665383216626724969370509650128327157862121275587666040290047452303859942885949047756404247033/42

Bernoulli(260) -521850747996151380189059639242126136103693562431225832506537914329594830081204070384876609583697459873476247230063862580288425708278688395667982496401084156505117516771745174732891193528263958397237247010558718773649505550120870152209992136323931737361785421705043567071393635797855524677946090221080900900953923217 3/2291190

Bernoulli(262) 6225500408881102797510043328034969466304425964851480796588968345345616249056035479080489691323529597769377127237910326626106353639640430862662758276037155818313797361926063056784629357346246050085674910484712331211955483400507386944492614175497512823803191508029088188458205305675244351279445756172428826335261196513 /1578

Bernoulli(264) -259790040816289605871057265894981852446821926693129183547995941809489012080370746890028132512470453552744290810102261593050521202809398000306194116349399794836747330126993715254119025467882141497980075978521524030877306056877056333375261474157967390906132257441403942177277395190738112438908312364218787710672732483 1409104559/374416770

Bernoulli(266) 7433378205465388942374346921315265579914317310442168171995314028009953929567334139763659272471378539733437299170730653893188546189098239099136195564469037143451800862626705671389885635044947151877063462456818869873419968784863413657781588400765166054615537660265187819984733697566907570502922002494298880159654047983 2623/6

Bernoulli(268) -181215287752963297591649028858266281596159320543301504003425598637697061538040

file:///C:/Users/Felipe Cruz/Desktop/VARIOS escritorio/_MB/The First 498 Bernoull i Number...

15 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/ MB/The First 498 Bernoull i Number...

Page 16: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 16/39

522696126018237983659329700516696739148841351912957174525785315414144429136591554131215700560325949733256954674813149699783016318415338094395743152932542723256830883071638325957369194991055197776850603497527503600109515880553950890416293 966947553269/8070

Bernoulli(270) 304652093569699557351582424227270111775477430579008410834478870463481039153775224667338604913378382139548609623914841564172219962317795636679913331453104140202134556279925445988685657134103647044753614334935369430918736361622260584801249

0292828963830868021774140963898080446961958927794750526681977409210580806334902 707423302910890705/73743978

Bernoulli(272) -538947928701982885901220044234332619235550901238216799744422193949920234058193242853372514032393947904799994943668224800124496715470710489626913668258239258211048497233940851082223003541243017289092565823015208495490382614339058885431845818572950688941724489137138548266065883489292508958450183325347653774440028386 4408173645832802729/69870

Bernoulli(274) 876921640102601760383168273082801324788039055564836901409234298002253995782034121007322766508391364331313364222035613918206397636790569250311165509441010945170696883786500399759308075144882184008248023432975450281978336106603716700929424

2107179248975708274982528930670627754900585633568069306809352009453263516817144 40032862515566687/6Bernoulli(276) -1388182772753480224524259543538426023294781120119840766760993950456297256537536762358314128425435909635398077811882539199662711471185655335807263675649242817349083277475519035786895107126764049407549359856712249235123586468592541328115099760851178135792262280438168965402774928136789551166963401124472782522202058296880872854126156007513528607131/4940319930

Bernoulli(278) 3288574272791325983707258196648395370596305758341699742238893225440550539879910098002426164478935667759666907669638986616709137799200377160559516125812795457124992507785560266265469172399329113247421069765604730822849303184464007727659407021486798188927253139176046166778181472669994161900278671855691024038916704559 966546186751742476372279/6

Bernoulli(280) -8490228242595311199119920565849009760217791023572798918266374350550246366225435144540895862924269878096526376888988896473279190955432566511173411205746712397692187887537779437718173050158951105924254322875775498449791436769311967741327489636985694874281460516082075289295724305512800386456299241907049270636679469815489106102786158831873003971980149529/7828173870

Bernoulli(282) 25875593499348128833220857256544133843109199942629172661571575831896009002717379314993110538912888759932261638883397790531299585084426973156913779915781848556

3115558189277550714226378727412391466965017246647885654192510025002480363963126

e ///C /Uses/ e peC u / es op/ OS esc o o/_ / e s 98 e ou u be

16 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/ MB/The First 498 Bernoull i Number...

Page 17: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 17/39

56297993421996811407029386847063439782311617981818206546311041142991312322619717261878315979033851316268092742291/11886

Bernoulli(284) -132959963583526612558423182997702578242047892089625754241387587021938995020766563989990185987109982064786136276402406795608981540644133005568845598733701027267134930895872207756078937107416605123323092749911180763524271940975157312568091937739185681066178901105822385739566191012805835839265694429000135104051173197

039224461050364993416415448157657001/30

Bernoulli(286) 1262786340764743836543650366374180273258073609841543441787781675688541881984249268360325012510167918286412665710785332495002470256724535451201518584261363284544626088778140281353574806840036456927404244048497506339393258324386379574048562781825209799628261527492591555049229691481538713081331723845462120745928641410668923052992096071568118182416749081409/138

Bernoulli(288) -4426158122015997656918081228667589801499808940970897924307086870252646875948841652238923933674489065786806672342321537012751674084821846458685429618183214525

289276658012594349154796284960120596423811831259041410965661717709958659062147534583171671141655182016580199364485449629732438469542501153689517957906763036169880300563526920600913900347892060168169080524563821/231026334630

Bernoulli(290) 158378960459933745353732673983377704622086418682000111407542005580986544145352715435649528631197645211762019722767661122078958064217177336225880988737955740461066476486097551548991955116319546315427449493825430704787375985685635337262886136570504412827663590990198163434342208367501561777230870660164068668650416176368657029205310526817730948015526849382859712055/3894

Bernoulli(292) -769496271232217048566454403451119653773906354892060893481293713784107951847019857310739767770463076516560575249619621659718985646126964039659981825577646225301189082287264198134787013538174178383958494473734277012586809351930781277345290942985827690026019144748986116319143448962997698665018791994064217597704711709748695678908604180272686662449493086793580970828093/8790

Bernoulli(294) 344977368185637380304333898730614153996525419281986770522385915720139215554847760949870834982202303432587625997234795118134923343663265548204594792841811439303451011251437993865656175552484850145014444202587617378736472160288579064961864004275382498994164923679644150818450558302750885234058860046684381556954878962153088786251490404112306387375170114820733240249707147/1806

/// / / p / p/ /_ /

17 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/ MB/The First 498 Bernoull i Number...

Page 18: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 18/39

Bernoulli(296) -1888575590158495996440108433926788958859450449505827069108529221911737605491094242128180304966356165162290173103044092702582217959772178183606221416867140355106476799094653551123469827906281690228047604677838808485752658196964935031379587556530427680306537879720377479310817318584744711522453387072627648438830200285728320936098194745411999104991803838665658699650727659349/4470

Bernoulli(298) 5683175611528696607080062478072501820703250802520963611339740016328084145085898

175251616359343168595858108624167762131679681416977895536025003761007598913177279789271071880600643885302907670572288368816385439218707793725555126269377090645484013184046265389329719449523663221529092764894703813815177897980268745011893371899061378940560801507189664711567121796987700152153839/6

Bernoulli(300) -1863878995204859011995045341848156066182191846635905937518715320655775958174360523134990756922303410810482600528769479642021001218415879006164302955370460829146434807964717737195356935144151583424833154250047747433575584999029126775186293388721514970183351129809976971603227633930434923843984829580311593372565398574762880028289167635570012415606941367995702212211519561707046505473575241/ 866054419230

Bernoulli(302) 29732914652005326308069038299046877228165947489285775398232775554326821654997284254954541436759755619186929818878962419179787160694148360451817997811323189321730570436847238527392204080083670713746104123180927363450365552833743396887002966884296848913481132785586683120732369858597153076261127975076406564459518695821788635361711463230165952857117226399909961673058570176834883271/6

Bernoulli(304) -5896752302971586952817880137553548037522952101385717862219869597959540714708235406233632122536677446426246295692119684486036889235399687553979484886254426933587637080451003789769961323298135257953657891721726854085498886402779031921701364180427128346719739542203363106920603436185256970882544947794042043194815113693600814746189709447821507079960920412101317160689806936226622681106017/510

Bernoulli(306) 689735739192864790938869842200448522491622174065530181755219067505817267965189978776569968680399983089600630968341102178380777713630583306140103562669027424552384203113812510243331805627699809267240054344772443480095752572066698167737729190346148297831547431732607091731942172905658944645576233950351675859756367833238423434368779109181349635099892383418900862720397266277623080279813067604999/ 25233558

Bernoulli(308) -1310028313878567907114692495908315703121191755911131111984360268010339291958527789632281425987720420051304810543373657881574797353695997625625576992435250954

1156474190755449447360548540157110742488736861553733277769463486445670491299841

p p _

18 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 19: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 19/39

44807198780234107278733859628145334731952115798551768101817753443736023659080348249001450368140437083583099127029870537678245450148711191680759214684176445667 /20010

Bernoulli(310) 3260606235276851195099437047707916012280054709370077715052312896011476347066426313756906147929976324639617487079038182718315850586912998681890040154101217023601746358548442139356881761209491879344448144235471024519916730280314406401197057752850694124801781598205133338269426259564611182358074475139266646779460335469

7005594348845404064852996320133446903527008500489356136774933641526013474789769 55/20526

Bernoulli(312) -2193102219234960851249218238084045751552157195198807438172621873598466768087209339634961932873204413121354799812430854107803299205525957462517069794529295542494092832089883103055311795833552429533447312406108521101994803478421832809058816063937868833476615787471103807134689008606266274585177357978207291010521137953994775163763305088891021061630677200039733393593143027498574533156207727067805 05888813811597/561706691910

Bernoulli(314) 58319632116552274690963640470008797851913569393851616026802699948792570800426514955313346203698994313311897550498332426841700731679786431087060191663246884471

122277787577844159566246144578084842125681321089374766303442405357411054156929110327670010300275581188558550579520897779108535864230775827818310605541571755550952336300769014556310739198880207114652836975369297328995687695253857459754731 55407/6

Bernoulli(316) -2330676203618095470723990230373318270997846858032509314923904005163414974525854459656213454096023152593544127001579959962113568241401538231186153459784375673085722714520062224650906603279528801763494272675490945823464526443070293052984245665308037854436521506646659698695360138599843255453570919691722935047844922140649650643216766436923947887297424791260110042630633931227556547559566964009221 6631914518917/9510

Bernoulli(318) 28122967090195287981055019523746421026174611154606607881410834553821571195600077156388139504050817072318352135336014937133504488344591033637378875175488860842142200215544952457462251551728305545862703146471647483394138505742989863336231595764600339418866218322681285266901817977284569573044604541872422517736195703069383015638214571378546092320911382385141634160156861783095114673655212399723765 743717305197851/4494

Bernoulli(320) -3721822981147963543473628721718160389675395897437503779226807860482566691214705959016239951890193486758232537597591642279654459920857716018601998378015710967458002507660860624568924448328452560808376796224541899685756821793434321138838512925307216420554703983171171540795387100799809353390519107647717976213032752752815159815739322121041527686676774334782328158773314452206678687770745486976844 581551304048486668867/230010

p p _

19 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 20: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 20/39

Bernoulli(322) 11947011202513683767723104489271471097868501873399758887514336934592822829976646702161909309680237660201998669294617552009638464244432709441651377979627696796385888263305915811924616794303093449550416640107641304231571552322204363229110497299236034396583681906657985198177302972578027688117382447661848083476283296893356637990999976607059658190271101386708876477455968880271181353449021120174672 279118531405266405457/282

Bernoulli(324) -382939382669485144236796360534598641464412319414905512671323836952119988303258

4377556163984602775965899294620028160948209504229098195604243661949859717087550540749941206115020546490009175884700307199551574107407855402424207686775155726579245497021834551699678553804651177095786249593672236240744422195553711332954204942399883879329051596664648871055498926334411033125995310873151284771962309916237507813788879633942447325937291/34098248730

Bernoulli(326) 1808383072515392862130370135635372000131626793093148880779287649928820293768508592707521055628027708276165829705670838064031068574527612930799078981578676791129015219438793213734036863426110360623900757855812426023541159774905365518756692026508213803668789819570234151094586211640196633499617063941661470860479560003

4748754276790617501738435096855283531518261466844055352065049361360267960303652 88231301797295663647612503/6

Bernoulli(328) -2038920955732166704563544675871539298534664548832344594940419211031004686244887980129990722833481906996574995006272283772989552251711645339529824674672295721387444989765197094356625686277258759887529063884063441729464466695304817154879753936013360244814470171255312860420052459456595966677396165132301906628818307744454944935388834925108370678592735494494812411438800013100442226704887804736057 100084506757161238437561170752083/2490

Bernoulli(330) 16450740261761201488286514086666341385844412580813949724000155038308870188720719658119876451207931032748030811189911338403495201879917853940007778344522354341186748832271809821828409298207968739139227014609598106703237472043228932298563800984396865943755795758369082954888437302866500408097109163018555655697695594114688192421141599313689189778427690359665256283948257291245464556741556264558183330312680675299274129472749543281530376155/7305236862

Bernoulli(332) -31404740573139387013607323899060788461129734403267877740839079468522117216337083625061725107066347029224470970177830290797457104821060170534363148276651160571699094881049180803660482733644591278636224534484481850814754420273709821201199908209760469191567840252247706876075856090781209456764232767086688491357087469900906692342923336064928179724546370791109956974800789303951709599892246386582961297095349501749155074025993332911366367/5010

20 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 21: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 21/39

Bernoulli(334) 105959450712139358561614326750678748291627849550191512662380413294068107407247886566713525350838198788534238121678429166419664041236233803606051817627731575939553790154021616196778501189528768078400811107009317850171384096998455082824610437919969197421385189475358775596537026092374519645052975059595487888618614275545703577191947383711761849232715855501325445057452043875112980841528855594013764288125280661970576229405994478822053767/6

Bernoulli(336) -110968358518556750910569006059104612436322304793290197896476208195051113971187304256671882613201063543710887491006989203213468862095728086421327649757926706375373160032479060881414285316805050049998250096629298691714712337731033133063244894833650574221421335477496494331790029997128928883270452912343595756835759921082499027715633187483508227173954421007445739076452215234463953952029377612275096135644427285378787750547213980148328191792731369493029/2203871994870

Bernoulli(338) 871667613876289947152259213998641324359438367113245978510277002562210922288209180150151793852558736029189876363096736208315035600167649273464678134646229708161579214485318416128870291425640987624153304026736765522468963515580422620761261

195314156252082303726799452238319359220112879725078451979791840912313059346932550771416018721541922207119333620480831014488368439858212426770461809324187079997350701358985200574078187666941445255865364959/6

Bernoulli(340) -139969199374294532188729693702577000000465664934371179035889932037927222630615161871008568258760858093560212970955512057983700284904139662988796471588843837914664871339017278834524915750717069973487760152722966363103180527139199261072959205960570607504345672675033426810959288741490491658133099197637151741354653719448795255505120643394167214213806837785207626077991226383344774422283805854628774864645574223075309564129905544107459811288704862611/330

Bernoulli(342) 999866869350557363722458479004395830847953169240152118030482972984856254139343285563059710426142001310818604300278555911104883557186325333153917124330048368249458087059040520529706556642732809436335612822769043297715578151918469336944179483860946506334004186007324467864842978559250174108263899703085692274142353761805113570952308838426945093917953996642662776561930695988488695006166233701104386823791719249365863288962981240951731129450241042813203/798

Bernoulli(344) -194356679464122366000063557526803181773780189986865586930470468471859228425694058504786433266248071070241357852997996746858465840302305980083294616549646400625576028335211891585990306706530443024292005212507923297176295319683924222692899007109181484350605033720455977537412753391449552230076184112225466977758107807

21 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 22: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 22/39

47446478661790743019087588298611993809224843559412437328287256779856482337754827908028601591041648043989896358637724179061858684905231780173/5190

Bernoulli(346) 2357481509540470157500613834267781473761111700218916888451462558812459108832155870047629256149526631642175073068175442689989038327676788740326748068662767626868596649367702307255453477048858648364206225984301573746682041796385480216645823296808238283621621206384489731250510555262637883050401445208843392623999725828

0111620289793360632141212087877945966075033938687737132829040482438463044913103827680386355585682702291192692673999705957317036687127526488661/2082

Bernoulli(348) -1946958244926408519819928540035312319794025231154312283846941445533833885684884185938663359749293528922631351379885288320544746558558870084671027543542465268801245629638273090846490014696481293058172945225573249920181321736453062629022981688433233577329127459928765113606300176648832109875139888454987326886636880988465878410619882237596781152380489370724295257792104332503696582825373077048086525583941198173749084587321884232599450628448598711165788748886648206781/ 56213430

Bernoulli(350) 502172089109637973079905157308517324166048351810351159422375337574332573514046742139861365117790762795398322755462389540876498686325519933386024542998456467504352201616875674226702066988781736776780983675270711591178536297327588046501114273115924942240089195877277170211145955479537604561876530663522061491492548171664129861255728492613537859772665546205365872403842851465588616941966018356565181922169705164734493393477247978508055348618032704534473742084629023675/4686

Bernoulli(352) -12359561245816347333610211154283867476483183549533150243177413535105007409660645839018994794985589993322495638209045465950652373385284290988635132496627468482309183354235563610377651291484274983125139258984606382689516336611547002063107605480007149663462290923330370699799512513012051585976283946919396000128468579127746706923053995361653453254989844882738707127566785716478776500725313908794455149509141863220008487339387394404640749069955014825600846412710922328376313724 7/368521410

Bernoulli(354) 44586958800126786790452414833451737276485269217604041493957832153847748776691019563443875873891685730191225792159808508144405955278309411839337401759278396174609624192685884123993968501104767184346477939067903846512439522927159649898761965816525286791728854346485686727420275292569511311545587705052888988969140031330003151200601432709893613802729701685072968681090703554561525613786761794587069881004247080811531298610122589066840923344874780872870506826198179146216889/42

Bernoulli(356) -182495206046873904911888730195578392542742158189419165572201483058631713239993

22 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 23: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 23/39

28631073000715354712349442824804877473011208435647924577393976121564194070391790525169749128982828132077146902780721841387850162775862442199934474879939605150425883830706636702361084052335568869843628198626221242494076538767614229186803516353130263179834649242288787960314531149564506544752097614513847899020629776701115098262552562151629993531946710430672386743677617308205579019072302696542508 379/5370

Bernoulli(358) 2369814649308935043228021398516266995926284111110247054687145623732369361843591

14116421846576636459712777920335379063477621836359011586413752593417899197603105681460352445932378792454366478006099883273862981279429149811312127273076915557845317216232626859123747826538028989342009113243530964905487060439628524659079587516495492222868853393802686849471730531810057511214889218773379759921377350465287299000379375481876741110444691063088672260104977000219302771368094730410104 32321/2154

Bernoulli(360) -778920925563520089023277887716919839298513486135455047496265119151473505464734957690937635048394537294415972122421086877478533967411348994474171388256074145035237797802154822761617528172700015731068657547092679836095543042179681364991968425138238530710252585175316218097390905698054739393609117605669741881868029805

237983772228322424502491583995084065878787104609542382045050185577023575049548616444750140539582676309391395859436260664778641733708499657047550739325300732722680932200039559718809/21626561658972270

Bernoulli(362) 715341102258098940319912343996707811685084551356244645540933308810413928160891724298276851619649551829973697033587181069271380692407132317161739109284011945227649892560360729074672778640720680874112214109997197387525352062913504682830983772725393570468326491083187300331970668449041594296073065276692887678729691114916079642579900288026881432235979137544823640729868705093774645241454622836223176904124630526882732099120398430089179339282190314646212515622936459121100998906 169917551/6

Bernoulli(364) -18399470428456050908014333117886494595730651014055636288722717429950917809500136272557117402977052839042105693597404693257617634201600598895359708213302738206862242849606975947076539483777341046657860376203296993121539300815161693660027527850273081527494673550440357634430596208643360358204371232957151165657607509017253243152916116719712350843286172274487990507840124030754833011930721808729659207188165402273267771908929719004881279785191361391914450528631012111465559730 900716078151518537/46110

Bernoulli(366) 2081324367967019740265786459470036224833310562873557450540774875219432921036336402990404549868392027478590439171188636829649122634207476093689178952995282835371286196461553693843403807963198520583831983015914878446689076557747871075041123908670727931411334042350252815108953825677465729289506737256043386826128593266

23 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 24: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 24/39

96437844619128850349843527450121343248512668807180114664932080245723088399660184314807010670380724658486771064683185071514502241671483171013576410513348441511 54035628560478914687/15414

Bernoulli(368) -110725230879881321879568054811797526267115166186538309029826133137308115277324207270571040263441920262386242076342056949047866353534514266980024412370434220187359560062050493440457221035440089226046696014690219122751069156630764313360960761587856716000690131098571105908045239988081704908481660126863809763243757816

06334943102133253663258729865339977292053566107401323967095342608874283325265349976365444693844705084679004587031711205053444484096877881567670717595463105972 8590843972403931253118799/23970

Bernoulli(370) 105436468101926712183015966237342027981822548065378183914917892056155580681320203026900330529498978410421348989042633250982811992039971268918718464971168941583528038472099497987423279686033847352373713634524328902029631237087627685630315840422522565122391280523543475578415123567558920642396486080328677738780748081096335514622972327452414694848941788411853785238697682675444724646915348071662104156310859630089274744684862265845975500290596918123665582220429778397569235238 1312064835994355860201685/66

Bernoulli(372) -56868988747972506254659596935683883463716573524427146597376366171981802233487630537261600452515928180502785214820124586232687460333822056190451678107485446400177877446417556715711032055230455854240595868388654451080202675047744244991416192115524025084813812227930163123287145588705727429456779082968390877093897979160965323905993195706278985485896440595636775123847679345910845046714163301325224520710766325936895600819434580574518875433796519293151389916795779147962584026929392606854485528272956190655743/1018290

Bernoulli(374) 272335219988441174665711644416817037788222316888226564189208490175239816964949116186510825827071430823770205468882164078844664808347805830968230876961416199262466469270666791566377066677591980435489655129480366457251098317170822303846655426605965362124131884076377822163533931299954525682197137509183234465716344628166664461061213432417726255707234519256021790376040458134340655641181955634260392208809071001560270930905476873636208670386352442356434023554492321216980902574 32456131056504444320853157345201/138

Bernoulli(376) -21144886325968847421136862640933605790730878065158231117894812330764874940817232709655287449203776974910988576503561661800249278991319113309582335281592647442495030553208258548341339318764197461147432848991686338242711098654931144304725148541437215370995347051713517773502906169174089944259231510484935144428438091067266131242394201122670888252772064856423958372374082615970685597386991737179844349495505700142239123902982043714578671787314293339023048726217119025452344630237832665698519639606247957083240801/30

24 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 25: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 25/39

Bernoulli(378) 4202152324841490851582198491734154054898910989229835692416027795481485467411812516892366095348619673337490550280425989691409092856177027846893427878738640633197809375983848427036487478678839362355759610808529212110936501477008097429319817529927993776215011685533261432410077791728458394351343228912812829117361997697793433448908490531697660725893829519644454139967318758247135377025444352170089166553939801451419735179550891309557305319624844923751198154628001739638691998206529289924753014269328705445340396548203417533/1651635762

Bernoulli(380) -585016197049150516429606755440285431916223316191798033687181061470667150509536113671258201054717866226570169976401850360230659699699301963057743166370714339259000981058060988677132844370590538962044247092297537672905410985648312911796535010450651733583075122028847986584025427113069993778348629306554503407744980050377057969061170508810412927919930789637438916383763636475443274955653725558963454824998976936559504337387796596709727547538729277633022545136032386860825147973153846428111580196229784765036789760566304701/63030

Bernoulli(382) 7863197960928934505546950111939500837911809651372358963456887700479992720249586

3945986283823608714469880713486237817037414979036031006235383025032476262083964387973243898060840722936009590301165543812264089314197515688838727901018644687053389435289951515626740339208758682375061416597195951759290458697298602770109818453665947288873748972700580769864649544946817207071904078063454972954577208463927530056857030200986057709786810533019838606174872050746460837475834260566055441410395805129523481902672214740177851314801113/2298

Bernoulli(384) -11075416275640217215301455016856697298487692508369326483114312754443271781190499298407724023135185062004544215897575247620943794500392129225728965590611217420829463050369195924100934681462677996141725794840014638901114092921099307567106

9409245612465372014808443841918963732454979635619634196765514065569765406021995951240364020270070411437377187081353045931837302854850452592893523482298799136698133585855070465304605234654821626817847160151252277371211732021978740981118935331815732788765628347320001270460720535171080710693555387/868841610

Bernoulli(386) 2879114883186609620826723532068276104139845449825894019948530676086618349883233245139084663416929458760597036667413717978530021472148264070597286070616857893183807259158771980877711836973364470227289919568822358886590073234578910075775184060367188577311832614887005612354400063672439629984465735358226535865532910705094242132700635264096296205052370626838252677418749801518077664289390262828965585623070897002640768910479324438878660938953441067263764560452279108930457475258025425810584201571774449957241464340109525100976383/6

25 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 26: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 26/39

Bernoulli(388) -21299114788094757397153706724714536413292077775222009197296487570276368549767668483739905654759629794289722059088574391474394384116388842393472198779890845792835783368209072403070166818305644992935634095949389005892015797599060514475400351300665686095027668428158520105490245612578226308332064019874832238296603858849991741989885454092253889660892754436759635904520725519771622791567806625636568537908996210911982475409155309551762403125143065067389753960600797968698009862634474184891040512288957749239742206998790145616588343479389/11670

Bernoulli(390) 1039554412204304060999050471842935871664238236129525031050621197904673190252061816306076783004652192616133527774723493749394461545816137751676691165637363944930483826319036927422553141330104483296290342476507053344206817648719129001417301179730182909494636606795995576156560517060235847592695182729113023238975218843912996538779543747649999358252604590089345118921257104639445913236211149024538216358616556115899687337155136781007563112551684977465108319504450250735437471011340987371661862741413337000516697089619657504784045957077408711185/148218378

Bernoulli(392) -466695632025751781692648017848987870271938714890023252252791233979618871440977

6663856362141719980502875970806945762712937180144475887677992558175799481301586019202060028185307056311432687319799854135340241062231395259919629305490635354239890090217072557890791528689479267987496699263598146171495893203013485575227547175970131771602894568516495986613037151863666577390670765165933422564746168996994413125484969251071189411262200344536746879649016328422523901374916569404613335757056186544409616787583076594896302119414868190918059336879970513/171390

Bernoulli(394) 640808912350356174378073333715330795309912947431801296035514496305956924194050478724997308276302531933458844716623312895516343306208024932183790655351844102967791249508631724180677304236114904329953319103713608769803340518450516179464461

284806009110502342220743568034682133273443656465906102058462073733441986152637932219455262690498783033366796807895595451968974170018589790265173871732540219203496470134837096254721957294282692027321105998231580155273075570903000709400332769684568638209079266772432973508791091418552966827434770217964847/6

Bernoulli(396) -988721621966561148765332193626328913917748393420050004369569387264811916954171227259914359919204850037848865164209491514082744037508971240530860484708097053877150205636763184912072230284654133188476251192712353503522179553028584279607562867103486123224635715566628419901003148442704056714596051123460682634021450708898416970075304559322826006913140287024163107231474177559429458771319865998406103691924416594616474259502957107184569578481372847337825034305923023606612708178208624164266478304393420250983951166030567160158076429357475405669518125043546 52379/233649143825370

26 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 27: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 27/39

Bernoulli(398) 10161900313215566319953421591388637402328180425349211048816698980319072816903521145345726221163084105611450343443221137527690722856383209708142471452342875346539666863558482835019156804751669116932322755085721460877938790181414341174421583630169802248409852214724801939766701626707662229904797008779706437578874336997303238218116573968772216970036489561373747407630110362020821819680854208929607112013855668348426244596961480597381595137016528270815603652018778457314919825182032768360703403384404569260876760458965758437801728169587522360995301639/6

Bernoulli(400) -637836392102899987100889736245882339465660750081315394597463772253285515127634023302789056061509659428612186547534409798551352250807515994557623033743228013767844748759035357201470841469676199651664804361663249151386523131611584591474384405795632554144028686794686434437254523165897512578873435193473769624127965433533785103292276403259603548004343727774698904484600174619641521274110076496631988736911883028507765498510954453196743298310327134328283669453258173529587457494121255252316276625903081894890171319044022983838553037495237790938203023796810 27746367/9315635010

Bernoulli(402) 1174239835539994552190497513182360535032387583605057260007722004883059102557958

144704940674287492304226247212849059989833910250445125922032127665436388239538661698487981932513000579577766999325929606223291472664224576178291713742872723127632853994169543584403270186239889883934311766077803787140536031309605772620994720158177432481254737877501095184402972656917745175226661913130878960138618730840741958163788195850901560843232573640710143138001159729682511610291187234554610346621711370121346135534129198492308718185558865166313048808914617330314355609 497/42

Bernoulli(404) -34590389184269498073201504849339569458532431595953504130530756011224705219169556649738299535060199984223808721679685660672668574010266703101840137966112890158844121346238967055265586337720563656945076973896008866961540151608623371400321

9411111793857968115791408542448654532635534101776458785227188431801015221049888308981666803079099223971749945727516451381541469207235665390844565364250294439462303313140081224224630513670992739333111131720597267189663118541748674779887133320822699283834465342129392489341643379455851358901161130937004156377928687672 5823001/30

Bernoulli(406) 1700038574411136210559247112182015814790609699737748235435506552210152989850297139035816916258067781750641530136839526175689236831959048254916715625977783948489406981000609880468816746791940482844240460969302406218096675526284028861874890646709957428032166249059917375958318607417675480137123914676205203099002413192532879436751290830927472415250948283769374025902053466622983908625626434360197351484526429581723001325163404487305065548512566437966861155244338246097988253208199536620000598997613474311722990494049191450530541183487938906501298773685541 02264664237/354

27 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 28: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 28/39

Bernoulli(408) -318268821678472690367952641359970352613261067423935316312625135469516217395381294839128714629790864646122696311597875108313589370510137848068555516473715235682332307763080949262669131513778719256477203343901233423138101383364932937892769246391274438233860145145026828827167093338865880475567374296304277379788912502912121648574410660679529719349753329363675265830688348759824744153091222213715437509402585792674523604890509950482176297969974096927936739350514323531304141450451878761724298365666446154163980299583363690461239934465143934417941810390419 43485420490171529217309/15755919270

Bernoulli(410) 4700237523350868061549257502287451825058021659532218811872938858177905727035789090975766092596120486501076415735767733964067941980107552937584140583420007585971015153942698579272276511396319877307623303871030533237616083322452745519784375437824233066312590235423331835306279920316360373436613582605583354521094366397210042201287111972628097215308255277428201531631010767588474159123898732952243207012499568558546979416687823061200971325229161591839419923064420216769552257473029576417555646398294947091294900249560509135799759924479804509908115765709455 3333043809915382015/5478

Bernoulli(412) -110407438267904044932245764047490655956467403301201804055276169397519662339870

126339584313457491906311197933497900168985674580179143184483519288034989721728829351302082076181653629234077289541324361645793146743962432061954532467939669342647947267041500549169372930162989091086595292864023659159340080525817986142928310878267738085379972925255016997550744184165687877987192200980757565927890596616420003756118628433587458866904707931969468028046391192332514349984198374364621162981301626524185846242758670116796140227287752825611059058867582000182177992 9699856406082793746601/30

Bernoulli(414) 8309660568168641652195632216912551725048162454271949427757784602972395740082546737232762807827989938785683765027652758740494686333474705454781541688158272725954167650714821944376304165451424558835320257093796237739184221912349795599927420905276026396594732607513986405801015483810141139719795422753630748113495270265802647391705032672125439779474717801188247496879173958128842461551576461668360765043561509657423031585900299162827086499489730231606734775907493600217999964655061613480173832252421790034503318509036471174588378925659998182238642696634535 94385683125383821474811083023/5213334

Bernoulli(416) -188406321746538358649682325835415560844246076544492383633508163564547804099213154896691530426404235719045836154467076874273276820185402062902437417930461531409317886771692493646762594583022318853261208951495220104317251070715910634256272720254460591674640338146619966553429024046780204638986663636233667086370843997297255922717850093318626963167296125792455986155618131625076654483870664013433299998182435119621095832650196216588831542319918935524790387650747655155154287843920508985561529956339563213717437665839108381119978136774613741524188338324784 25757962198139801618258600291701/27030

28 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 29: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 29/39

Bernoulli(418) 1779488290712443837484612243000477379544392453663939988149541576668372900364425482375453545596542481407626012350251240169566885710543317099275115688332095543283009420886875758031587703527789029468004161940923641293689608095071366759449465243555292713915130958318338340952141414132018724435334652593385590710602765340816621091854909265351151654290176978895221234263594097412717013598962357324908272881532203523119778104883289250434222969337541750731779484259729502469444932712004234737932232132721483006894186620451211405621853101169505189675852069953799

39580805302928813353440147414740763/57822

Bernoulli(420) -6126914449391766463123273102284652981370509248391971126816109275821466096976801669348238710361647712578179757979414761992440067232917335164055107920780363262942782633482006999971350591213671109122331751122081373688391335194625200099100643843244514246383231743873282258287892336340426940736781587230644995704054335003998425945469627545685623200550970324534080404065484535299953386337281009271537528001339179644699195404880031646796095372570028624110131487675467842335793522121252328612723178264941963550114480615755660790108038424472918326815297861578110970433546154844146996383907171442617576638221916277/446617991732222310

Bernoulli(422) 370417641649773203811105792421530317349989434553176611030631322780037740921920903496806496686319103807921979015270437429241936687918394087764863038019578527638851481686403847480960464641545840936004289242306394237365086284210791291343989458767793541220855587660095196948191905734357956461535121861354233393019487098593606068830314737953863466706245485662337370451037774820208643752612698330292374600196793018724057118532300846184682702881492970790966220893763118615367891028920559173128847556946881708070136133779182213573320504698972245409107308503781210793753700634159761806826499289415831/6

Bernoulli(424) -900309704889057549412703055487959300250691255243632314995356843469409197586598181836315775665695203810817228257767800995208832223406044287944134381117528642679552487333128252142131375359121793415508211496537834167452784284536412724329064314223405159310288664698829339128075019109308684058290006604682848685269913509631592635991061291910848588896849609801431590823098722376633326783362640890294817117428008250878447534568070706275064939211743430644145531251375121140903646902567865610094036531542192311798685900713287395549217317410664958760801352234360088468504559813801913565013476710034147368107/3210

Bernoulli(426) 540225378036603052990346199510807018158832443697480204250735647980528769665424434313990872758579010452107244811015945468601296416203994681028077935333710904631550194393763004260011111100825548574063403788483396960128246802587868245758939

29 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 30: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 30/39

53186081095194738031315027987901599699063076400850373460929533644671669856383541718682959908309284048987253429549866158169260473899283324734840555471844451471581906629081405048357875350755464695286397907639138344100989311969291336190793916170606327076279174475858929332637620247498179721571404122810497608597392310341741689230018260320576738940580419471886026121/42

Bernoulli(428) -178631832601908536171004558032761096296603555642069337022466657948224618220000

462860819307447255038425012723042570990636159393162920489265496945881843415223197089039558399046230412722134470564185454526546692168928856644009854678892565378884116563496393911506002791803756925372034984042436244890477408434546164564440123159575118382731762120541349243900708792397436983071602078285813659425066659156365690242457074462226267478374244243395380526750495191218544888861880143020865916520055167383158922400486128739977249726236354738468036532667283720083951543434880992597829033564904575040629182418739065389001/30

Bernoulli(430) 79145242800039505299046367436740877464129927716944938227579741838496366674364770619996814172657769987153562064787727168037101136364172587501644180400316270621

6814077280766553803448788712737779201122868425785256450531121303233116813021906603098871081632396261587905577208955217566658493203885877312418398060846091120975165767009344894679683148265158035296420969642632188332444968324025169811975004853721487927435823390089679208323886268818820308870377103259885100640557295098484358112295185600733503211183865432570364543715288518332255545140994972346903247999234036372815320143622542006284391778075614230370915/28446

Bernoulli(432) -14750577990707069090892640643627890396790588057597932870361312797605339877218555318290483697927533647647152620207786705312787195868985834595937926758107692208298403338603695989231215167692521223914659443461688651180043473122600527834618929052569980773595567060954830287077779819370475900148020136696922033144977602316267162377565896641961582226753571000379259049438007003714263998786954349001656043288757745179230747108219268158244213583535560775121257993743283335146172958812409641851314398652207671071800026121000251318559834563893238437683153099891646143428578083417759291169439869395337214083816200847999672131739013721/ 112409792943630

Bernoulli(434) 374777948723013249190078483967036070262196995319721004950125135841911814198619011549356410270085469095562024553680419264421054828395920348232957623922946064229211025115849670614254096564246170554453262384472539133699367436058609043489926484940433001535924350976694798538284096205775504449181934303253795061219432435260009742614505900088509170788373024679338732454965657850652041060078316582665978147857775596653790453928593902453563143158355566291115657291683041742729879139

30 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 31: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 31/39

2192762504813321994018595884981406242206002171583618182559028568019214315784771237935918859841167713230012475726056827372638626381963585567/6

Bernoulli(436) -900243602303872329265137769673233267946975216990147426234959786986060151151172751639380364499251949168487224779118186396491935860170406603364241907178142227791955763742401028085951157594491451096283585992115113068460460271116279766996042964660386482546289139684757837536311357656096827258440550754675128600333196327

41902401109514097069147699670253945763189080474357381924555174022637039432337932007567967360013189225484557699891500723386807516891972255376800483482791579348941380904127063436404359870716285253826928676282091132256974170075250937201408937099856598602948280585945432968199829410867368026769199252595801/30

Bernoulli(438) 26825536124633712636777822881525954504586843102943784964558917892563879584349741427294516074951471408416542656112772500549303981007948045251729020749818520071750966805589268354631881566534153569703280810679763178186707977863690061737638205464081759839403867615351703395859790997483054431124949085312227009804578356302689956605786207696547850856758744987704156772907613971863685498106666450789705

3160317558190734639340443419436918626125596334898307900637096349388220502296543130848656587202710882968136604232104512201075293126007959863944130551986019010434312311477565523149656237135607816533477227160969517648113475415388407/18438

Bernoulli(440) -1971549561515498045945281707781358725202052418820469210287100375124408635052889958528421462206148998040363604314916692108315970766317682360194568697651597939992942608607863240436440670587263898825900455009148047595679837461799849465343687138591048044960789240368282898014290879082621858961237901928382366671020037189395193173411370422088058940123720113875828797411348581899556685938975754080936775135639140747303520886284176117348920517204041675362641162399925576576653291783247744987573436710429594592096815313807926352292662762861675065257056115521036077036706726455044401225578559120921795944351508096992367201543994966078858397 /27695910

Bernoulli(442) 934217844394639862121876161182125782629662966798874841047916685310521671553962326103991809647198275117953002131456853984058360472753503867675200497447364861473654065939291320525986944570166180778722315422080724702421323386482784126733369118721815203984881266971497573448614086191554625693617723971683850141789064565402372607797348631247017594179350444633051496340472506374723019936564961282558140233726105870589191017887960191293607258806456016263231512800235871497605920995641449875958591869460832774676734017514779283735936104646380107986104389604327378999649850427118391694149262577932479289635308490619974233553612397882181813/ 2658

31 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 32: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 32/39

Bernoulli(444) -158845135682583637310050414378214595799174539534413035558457927180260655307343938945950776141757261524377755785578389794390713400424204955224064287421714210308705949074744929596932632241358688262813726174958748320025797188191224303535908875129465586234092629175800592249211106320935394054787272761311671502199224520443098879151573888801771623192883526328927129807622792528335792700318705689540933290598347707055522491251314640804320693900281215224262309217387438431268666875059083616022905739177343532424279695920452691897028237708410245697642781733124

3040621040701066692022628883455777535731782517692198800045655789245002604555941 31928657/90709710

Bernoulli(446) 52820988550912804071451884491873707077611397679084704441786148606552305037050330902476831330763618274617948135285949957728028695870688501651855365293214261665763024004555565085202897776922988749231163862901818153108264790734253251559229193150038194654616836673701295399639842711610882623238385854157477150420529686140635722118527587063478286467506193498289348590140209058848431175257465051090606564081140432276211107220257560552836024246626312132223879207171064190421730933829702220468746118116687590172977326777807226148473634828964585294322560361223896420954749054906526495733099883401725824247665659378641424764700866014787892724 263/6

Bernoulli(448) -3350996956031095107767330038518293917312021823346487829425219388021617448959317350582383824661705614558588255570686045188731367535784206070621778205976288528736503065897861516827559929013835246835478975725900808964854113754734811043908981567276832731318047353479688881585185631339464442706226142252426539951145172106907340929315838278176817225635404777288904422523050751081148273763467321038114210640097494316060573957181050705033711440975159916790647140030778223395349000335262289979315142280206663079077327195907867647088343222309801199919729796704850728984223819905175418923101449857176257365526643718796966245182132806035007560 8863875769571341/750400230

Bernoulli(450) 93910555727653753370843961173145578177181801661815091612715610591294435893974850815130184247050714742061741666390823561814548294440724918778705520626940593788497709584423222234638292709899017504681446091715162196489027846387121303725697139987588942264031544373645462370469362344868783134447405089129057599964910854063135296744002251884712439458506415686597106704022709694308050018948429224404426185580165424943606612688675973311765475548319452639404828554097734677887165719462354933313629530651361969253323925372685242818126601206869169075514560717180590049005629401265156556384588380171797824335512033857360319946216406263295844866 25252298313721425/41089818

Bernoulli(452) -80367886003297896375549054086064347511517633438276369992393735954581890880122260874430849108699364318031062443573127550909621163684824752766942529058158885380840632238599715260765992393585071636995085421789432768541505622906828564235089

32 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 33: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 33/39

00798777112787185623445870747150615150782172422604213843730688721433197193927654307261557625517124764287228841421171512634534585391620401335799765458353101463743603983062786131145017655611914534755704275915462765633857066185411573999789535405190641054970837982446446314245641839258145246102021303507933166787126508119006984137728812640057612823780541560848078401500756860998000273851310662643557 278203530509156427/6810

Bernoulli(454) 3688765109519035939597863170745089770155218010432667512091960969482056064803047

4979171133539537862210662044736026621541679008373532300695155313150561362479551904410240432070856446263923979299500092444516028968803538104878672539814981236198854450478175391010338000353791751383268673072000938944246515277386132140583257856132696558562847161814996976075174769694748695438632575090586824991284249542651404132205213670261425227222486264304182560679963038720949995579422933796694986011135385677383318542530506241731018476230796808445574699332521366132935744942092063737117719972419446305379041821531028902499051591918182645467840089773846 410376436748099927/6

Bernoulli(456) -9231251497205337786805280106627035365614237424730160108604924651736976180075798896215248792654225922031690989989936814428616639799004585592248516552105228745

115600772090469618649949110864874437364870818222898493364585027928374556652768749981360929058298243205794495656723748164403781748730579086335638752417431277593473211309077070359896017274789066550552469547698979828077256389389589765286385150263946322137435703489322701057413339409715907420401015745559280769997899350755949293570194811595617539775432300877948131084500469766803745905331871839118178605120693482483577762003279580322707699760471279269534859347690610372106577357727353920929624706796074041823/285702690

Bernoulli(458) 10278256353812610250841375095185649625607284501322235395215269488173536361817026569285838288287174399415824498776226697074299069342885522782914715189138245709525532343687897246034428385673181414416156552576768121872399525542179089484380761783779102255604891167488398869694533376953097816844559281415526115810802169419301929685234168971950637625385574092875399806612568940093924080893589154969775766272251488592364685053693420034804283667985693346987062195833963977570474224666745371961929522671808375499017104909353373091136768904848576025215447733168212750846479275096027317879898547831700811485138730854440587419393609265846843555 44622280387129474006982319/6

Bernoulli(460) -6550760154113509955322519520324689762818345309330319372044343946911206397745316500483812442237014438941335293944750087907405849513426436624910542114024406950056919447434524096723352448017446297358873710248617421245570015225121262135612027972284197922153718331776532945085169610851088437877134878008919341980631531214431991715959299563428081327762284421994333768251921757188656927704213872171465

33 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 34: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 34/39

925501861603885110199062495929817244864046765240300372782070942306808931353298237329193104023648523727135025613272860312485759776097808925561726646874622086120677449738708016595010877049123286575216517173385795826972669505322466175106064791167244415577645190187783109558537/7150110

Bernoulli(462) 63688865888558905290155731572702433298574739275100550324480297997667539732777334907438024811312496845744805165367073960643414011348316887165278129554686424979

95612469570965195817160487421985680788793411096140356661976146745150228102075529102340373723482996983265766606390143860966670113764902836475227042342140853703902690953653738071098617987052339494008437294258743953709135498602090607507693690330811502343804351805921729587694688949530767925472547494085687987805410410505963373499481785590861551304643751957929639863906451583045448988420712969430083368919548554903489673904877295745230080254098114031395040280378645921227902389659674535661931328259201472684713522055433/1288550298

Bernoulli(464) -1885729883017997492411277056154161628122122138418950207666907626497604709280832704445528505726439561144972157526110477873041093751758478056951517845321848516

20320647579855705925496701761448465808354795813973779680808888167818764964700925538842134054390992956001669225520942778629366261309269472085949866705644243058822229069911401050274835800403163105897188918692416516840686738234446171587614205164199212128303162013809506690718962024295099161224082167003915292076143373222944136866167556404170101140178710147326875675233494871699877286279336655831877302931691870727029196060937873178589575033953909097962613832380524097498719417990532304114093172036385627503846689476887699/7010970

Bernoulli(466) 413664867987222956244209355804553132010737311619873937552617773013514076367023256312176160835062661892330568050774492900833764272232882273128949537336490168744752502048943049241434525025420643944559491826884487174091266835019079457750298308269731643882842579624683236689298288625957015934020852065186333120537819299541510992711232749590370342660947186143661434743740645683801183663840994358198551336011498396150912151423938206307866725487635171065947029616755552973030152102744795495331947296938243287814790516243968203740094323906300807997945263580249967044922095488324059855868304323339162224087731767838889133184638682384777584272685488996638922752221799803151101166568141/2802

Bernoulli(468) -103110784171582925834346391191203069803301152693724835574305668967469760272354011299017295664859006303114326060072400434706502794750710048845059339070559509653738427255013456258080903668934666472097301930610763674223216550322369388413998637420436998154407765681116398814947925836989520074635968480325415440112462267

34 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 35: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 35/39

8491322587940166253688363451761279210145812935556959005617096357884154904315169217040557989251752098016262897990226072225936970292748900280469462419239068829802849814616525273947160256662458312243507612184481586372693712226732955571148746164223940290646509705984881548422992991644255618458312931517172972824955609103863870050004830358982153156128215328921678827090764016307/1261596819210

Bernoulli(470) 3011885126705744099735220397317997743322842379662843867012457485654061644286810

36128926063056095855532173991462477799681429260898037617758622985941710976235577943559100259786932475830383970536995316845412258295246742979426181833225367398491810295210078233611825547244385629725708901995508766557190851612705431746456650510895626334976810141560416672624945285953742157497174172068239724208754377218814505115022247180573164262593883452362474468782982223281207823275802362572430210812017251300349771480681113489830696638136842926883664618708287688430079713258060558978096084995295625323965331459365135957743350303225791768643943305879602716567061428469743627314569410061103860282955485/66

Bernoulli(472) -770937004570847542710916650565931789612450235859854061364164699012203056638918055135259895416107273426948797500232897203853071790393885116465171393875976673693385000879337198213556447794398434782352654738563122022624642967864571454383814267648876048449590603480115693689162580755992686116534563663816203506520969500954741353683081691871170841572853932684457019190727452579388269518761070066012225637906766598808889134766906870857170491069727522854987604110140202165701028056317715546755482888281141979064206161119893213557441124682697844058662867837317718568074632672139404775850673801367503450134341628737627508058275331031355246875710092188894581462212753275513865164976897399277601/30

Bernoulli(474) 6129522921698903924225094098894493975355342495202583967070268649960491527425425546286128994652359747795614576729300901193288468364098351921425898605865990737737763196859623939630382031884908027628137877044490771874628629780057338048896492947577968007519815003168246395643465584343043193237880881635998419368585273823574720837496255282601496997088803126305575254814207239481124819310777601851780008004534530982225452330277362311532174615219685651873091360796309808900938980799843045197724124205459703692404692815206856959614667498156439854860378606039596585529438689777885628862162187008631192421450307071680585728728072572580947780239520470275779631590328798136283209653623721740978652009/42

Bernoulli(476) -17379423342300736405717844177647822047732929524799274624619402803309895539459843486368861521991621432430102300109335789374633008390374420499116665081206184142374648758717528679082279957824121275749931210032364789980185681658781469425053

35 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 36: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 36/39

5160608651214203178715194330829602196319299830498255481024809653516681647938371069642056989453238492194899464534194575984259211778777474726825907276342679607943595029925764974686120493830750858815144111018156639748863065679944594300279690320295481014774768770077734050367942856894507914571711299927762683035011101547081082113463840150439878440505062095907817860452253434600485043521832982039217192780017205043143542812887267054217968944656636429743815938366731/207930

Bernoulli(478) 13873674832923745170636547493407974778812031787162484396922203584245099363875266410392579249977654901546226138255725682890165166445534326211967788770965050606335620329629392266509006667636060346080828403980900870728472844701200849051031032721110383896992993960600720447264177011379489696922012639234054945046493515830646916075528778995875263891724422324224871104321292779816866047869594198817075501831319907776354543266924566231340617726210269713505336228589002649382821152876769886796237625064939931597087898226387660507299139385252112368241337865982079462586705656758449262979906152409703115811425535504703782935179149721682887228861005266932595149810184020272544138033841220106232249961984874041/2874

Bernoulli(480) -26012984231082938122321205711106137025736836308811099420978321017146930273005671218213801512995150233049010223325808387207760652312185884489040204754381130425223206104908949348483694397053700779323806598166397483624967026385155584314813089275200872985931085543928822164664368156111249818285706698582816847860316768251385568355911376789419906820360322920270272727732554866797105317523759568495736021299387762599572352567156747373223964524139683333489545030164669822955224449969772265055374313158826483073058617899550929715104043848380098396583498089878468223019258239295983312553586622706514962679548326500707178484227310027019877548445744372693423428185302230083093969160616600533454208539007576331211435405256 579/925269860885370

Bernoulli(482) 990616118004405209547336756803741296643221987382321931721822820900299097210222317336001831102939236490395767769383589450743538317573906480157831910388399026009549363482047723522295682385225255084608513720106406633464966275709378145660935302980557499077874664887504148114522460257788204486783699727500508138689641080038916313291730518751063292404119140988768624151887967557709255327422581104429283482510069570158085040668138860662778558327704232203358594262804010229103345601462990376149249652299540260177492690219461257167020609270211173637016502365724336529333125021542322561542486553234490872949324335738034611680591470710376104053043734142034650737431499785882884589522913671849942865299633710178111/6

Bernoulli(484) -6745839219742438067275836266057268933050012633434702778476441413537112837191447483962146434648155277200511766368378306412027150319125585457512722659634591588

36 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 37: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 37/39

32678711777574436725109883048688054377892408030247686556398952252471378342025741011438575099484896341336771053946168596117603779433009583486087778261092733102095362575294914815257723299413552987428930625441349976483182063565793384408266465380474529520534826114954047630754878668040735849610788709880820541989250906334800119386014176221640220454426941644202670624599594997416757514254570930031264863092952803531973860879930032899029342578124854325385199562765121526103213588359312368828453688417972133504757523704888418645741605357575301183566273541023/ 690

Bernoulli(486) 369763997577304898527792056092078784633064579850215089906718927953975408532819407204558577594984146089620623998022051043813802512840569387856574528038951679028036813020229062675066916989178254799161955591299056486170972788431152654760791766791190599466061280142672740585701636947897534361260451582259758691868004875864277790983654375073056163053627813804545640618169241729192679530964042280652574338325670662894789508966565337142721844903092886592945025900894162911247219665577745221033424450158824779569415157792860757313903143859765449917326253963605938268777389669269349544451932422774330893531316131993509969738757701435869993709233337662014445697606454995935095546520785205839498933104702647973917548450654 482159/63346038

Bernoulli(488) -10541816873814096381316169108539113544559806579137816926164708551453053764421674476779663590418587721548805288914617597594086705240368673303934588475540778050221133715515127613013536686418819433156406738624119864020847059082718330372484411485597582033736496792901481620093071040857138614374070277702490846650695664248028186959784027234555083365255720079247979950886689963934128030067369716278895226180485362879082526221980577215262396385617524132279613757092621411332044486165677804146252629352839983467564429582144636634184191363198151813999632307770474159980792200412996991870674127149512046516569338215208475275772897223820007540638044339880428153723968600215159459367880594154570049177779556101898534322340 56001/30

Bernoulli(490) 490708060345718168482949551065008296976352341812156850912460754793773228598743021163789697895339848508047563198613297970895771272423084451586762411542433689884882582217920150615320261296412657655420294950882472519077107436411891314989684272827405143453664676299901282427746214002776016429289992734596941647026794542862610180682813869753438462413802302318288921935542654412271101075502309306996459972517715826132089736597584320511669263794701105417099176436055541622722611853665479429929243382275785136760788118477444370781356616739167758192241507716005871662971992278037186350173271291067722673038829083878521474773044108789762491726385320922397469619970046438378452390321367551511627206765616414040686450916033 159995734945/2300826

Bernoulli(492) -295710682036368660462889828594612232955924955002201524705248520206592222985898

37 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 38: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 38/39

2084685644090246435526633192173012792794565995151677276251506064500189183973658668266255100038378077622347219072292689397282607532095789514858323583796617533209050969370549540982453282828388206120029279998278753379433675825020205456689565011134110012795554020790553928876484323963572703870667305141185935465614396039197787425595120159014751464761231415642432913279094285052270811492908973848008097977295940813077959111257610340633735603719103411193071451187937622330746267759089146576218753118272733193541604894250099756555502422759761995511863619275251

1984670039590742279929660651924836984103042578319856732472490503675332043765960 5858401058641353/226590

Bernoulli(494) 48304952056070024985817756788239978908682438355340656791822950062590796355241246689448963611728938505601369463215719576289607035969877364225474402150107267021033472617633002498666739540719726067208908400868629471652429458078768484626439283884479517280978247192859399400878296914805548929586054952054550941690046726387385343252474507896205536559285343999286125673465838911018803676968634234058996143076453319007358347695097769648224143191413651220988411012365741972645136470905240747776225223601701498704103140362659865756058524036705273180849600017203422636276522059566343973347678362590339657974928808786150211385800610012387411013

1952296752950967858334783924239580399180961944584033318498429180899446799879356 90252652536647/6Bernoulli(496) -2553510922224169897269417319397351877471624217826587723427907815421830628819045357439134534960702034770110438930608272764066224932899475215437297342236199909271592275963352127037854150779076976335745627637872659562645972462367960391557764394770047210667359358311843696006289416640231286719037659293148046402280224096743628693000309850908613178155380833593357527288836140271510778811315428799638586148620725753189922276076274708675847389439636021759458438765688723107181114564396011162845823277525352598381790749640760035718291974416252381371219543613570303881661694750473664046507362493822028234556663180814081396903739657957886366

3701714202683178828730441933582773514024218332915875259194767588507001149870106 803558286434937883617/510Bernoulli(498) 109865122848151584611673560594290165754441894276368560548381912845497638546489943473724236724095238506744474900836564256806367057972840967346175127292454912528560279504541320374184423042635861675985398329422741182189709234833344612099575633961637349062044653629889016751770974632874287029915736629535639003257698478643655378973595019757875361471141167104505491430542529353951978597591329218845843547284003410332653298426772099783819705741178585242260541458732945989862623831443160498317466595792069381575522773601354592978160307298563892368832435529933879136847223915909126311223045236240031443275276664068708400030822980635517221018152497164494285989399694041087509194064920210610906678866380762788743370112481 7799811432100659519242101309/3499986

38 de 39 10/03/2013 07:36 a.m.

file:///C:/Users/Felipe Cruz/Desktop/VARIOS - escritorio/_MB/The First 498 Bernoull i Number...

Page 39: The First 498 Bernoulli Numbers (Plouffe)

7/29/2019 The First 498 Bernoulli Numbers (Plouffe)

http://slidepdf.com/reader/full/the-first-498-bernoulli-numbers-plouffe 39/39

End of The Project Gutenberg Etext of The first 498 Bernoulli Numbers